Magnetic resonance tomography (e.g., nuclear spin tomography) is a widely used technique for obtaining images from inside the body of a living object of investigation. In order to obtain an image using this procedure (e.g., to generate a magnetic resonance image (MRI) of an object of investigation), the patient's body or body part to be examined is first exposed to a static basic magnetic field (e.g., a B0 field) that is as homogeneous as possible. This static basic magnetic field may be generated by a basic field magnet of the magnetic resonance measuring device. The relatively high basic magnetic field has, for example, a magnetic flux density of 3 or 7 Tesla.
Rapidly switched gradient fields generated by gradient coils are superimposed on the basic magnetic field during the recording of the magnetic resonance images for the purpose of spatial encoding. In addition, HF pulses with a defined field strength are beamed by a high-frequency antenna into the scanning volume in which the object of investigation is located. The magnetic flux density of these HF pulses may be designated as B1. Thus, the name of the pulse-shaped high-frequency field may also be abbreviated as B1 field.
The nuclear spins of the atoms in the object of investigation are excited by these HF pulses such that the nuclear spins are deflected from an equilibrium position around an “excitation flip angle” (also referred to herein as “flip angle”) that runs parallel to the basic magnetic field B0. The nuclear spins precess around the direction of the basic magnetic field B0. In other words, resonantly excited atoms are tilted, with spatial resolution, by a defined flip angle in relation to the magnetic field lines of the basic magnetic field. Excitation (e.g., tilting) is provided if the B1 field is in resonance with the atoms to be excited (e.g., hydrogen atoms).
This magnetic resonance excitation (MR excitation) by magnetic high-frequency pulses or the resulting flip angle distribution is also designated as “nuclear magnetization” or, more simply, “magnetization.” After excitation, the nuclear spins relax and revert to a starting position oriented toward the B0 field. When the nuclear spins are relaxed, high-frequency signals (i.e., magnetic resonance signals) are emitted and received by suitable receiving antennae prior to further processing. The receiving antennae may be the same antennae with which the high-frequency pulses are emitted or separate receiving antennas.
The emission of high-frequency signals for nuclear spin magnetization may be effected by a “whole-body coil” or “body coil”. A structure of a whole-body coil may be a birdcage antenna that has a plurality of transmitter rods running parallel to the longitudinal axis. The plurality of transmitter rods are arranged around a patient chamber of the tomograph in which a patient is located during examination. The antenna rods are in each case capacitively connected to one another in a ring shape at the front. However, local coils in close proximity to the body are used more frequently for the emission of MR excitation signals. The magnetic resonance signals may be received by the local coils but, in many cases, are also received alternately or additionally by the body coil.
The magnetic resonance images of the object of investigation are produced on the basis of the received magnetic resonance signals. Each pixel in the magnetic resonance image is assigned to a small body volume (i.e., a “voxel”), and each brightness or intensity value of the pixels is linked to the magnetic resonance signal amplitude of the magnetic resonance signal received from this voxel. The connection between a resonantly-beamed HF pulse with the field strength B1 and the flip angle α thus achieved is expressed by equation (1)
                              α          =                                    ∫                              t                =                0                            τ                        ⁢                          γ              ·                                                B                  1                                ⁡                                  (                  t                  )                                            ·                                                          ⁢              dt                                      ,                    •••      where γ is the gyromagnetic ratio that may be regarded for most nuclear spin investigations as a fixed material constant, and τ is the period of the high-frequency pulse. The equation (1) presupposes a constant phase of B1(t) (e.g., a real B1). Thus, the flip angle achieved by an emitted HF pulse and the strength of the magnetic resonance signal depend not only on the duration of the HF pulse but also on the strength of the beamed B1 field. Local fluctuations in the field strength of the exciting B1 field may lead to unwanted variations in the received magnetic resonance signal and a distorted measurement result.
Newer magnetic resonance systems have individual transmitting antennae with separate transmission channels. For example, the body coil may be divided circumferentially, resulting in 4, 6 or 8 subantennae. A different quantity of subantennae or division in the longitudinal direction may be provided. Individual transmission channels may thus be occupied by individual HF signals. In such a case, a multichannel pulse, which, as described above, includes a plurality of individual high-frequency pulses that may be emitted in parallel via the various independent high-frequency transmission channels, is emitted. Because of the parallel emission of the individual pulses (e.g., “pTx pulses”), such a multichannel pulse train may be used, for example, as excitation, refocusing and/or inversion pulses. An antenna system with a plurality of independently controllable antenna components or transmission channels may also be referred to as a “transmit array” regardless of whether the antenna system is a whole-body antenna or an antenna arrangement in close proximity to the body.
Such pTx pulses or pulse trains based thereon may be determined beforehand for a specific planned measurement (e.g., with which pulse shape and phase the pulses are to be emitted on the individual transmission channels). A transmission k-space-gradient trajectory may be first predefined for this purpose (e.g., the locations in the k-space that are to be started up). The k-space is the spatial frequency area.
For planning of the HF pulses, the user predefines a target magnetization (e.g., a desired spatially resolved flip angle distribution), which is used as the setpoint value within the target function. The suitable HF pulses are calculated for the individual channels, so that the target magnetization achieved is as good as possible. The basis for this calculation is the Bloch equation as shown in equation (2)
                              dM          dt                =                              γ            ·            M                    ×                      B            .                                              (        2        )            Equation (2) describes the magnetization structure by a magnetization vector M in a magnetic field B, where γ is the gyromagnetic ratio of the core to be excited.
The pulse shape may be calculated so that a pulse with a specific length is discretized into a number of very short time steps. These time steps may be between 1 and 10 μs in duration. Thus, by way of example, a pulse of between 10 and 20 ms includes over 1000 time steps.
For small flip angles, the Bloch equation produces a linear equation system shown in equation (3)A·b=mdes   (3),in which mdes stands for the vector of the spatially discretized target magnetization, b stands for the vector of the time discretization of the HF pulses, and A stands for a matrix containing the linear relationships resulting from the discretization of the linearized solution of the Bloch equations between the vector mdes and the vector b. The solution provided by this equation system delivers, for each of the time steps, a complex pulse value with a real and an imaginary part, which represent the voltage amplitude and the phase of the pulse for controlling the magnetic resonance system.
A magnetization may be excited non-selectively in terms of space within the entire reach of a coil. Alternatively, a slice from the reach of the coil may be excited by frequency-selective high-frequency pulses in combination with a linear field gradient. This field gradient transfers the limited spectral bandwidth of the high-frequency pulse into a single, spatially one-dimensional, selective excitation. This transfer may be provided since an excitation takes place only if there is a resonance between the high-frequency pulse and an atom to be excited. The precession frequency, or Larmor frequency, with which a spin precesses and with which the excitation is carried out depends on the external magnetic field. The field gradient is used to modify the external magnetic field and, therefore, to modify the Larmor frequency depending on the position. Thus, the high-frequency pulses become spatially selective.
In order to accelerate the imaging process, the spatial area to be imaged may be excited only selectively. To achieve a two- or three-dimensional selective excitation, the k-space may be traversed by a field gradient. This selective excitation is analogous to the procedure for recording an image as described by Pauly et al. in “k-space analyses of small-tip-angle excitation” (NRN, 81: 43-56, 1989).
However, this method for spatially selective excitation typically leads to very long high-frequency pulses, which in turn may lead to artifacts in the excited structure. A further limitation of this method is the power deposition per excitation or generated flip angle (i.e., the excitation efficiency).